NUMERICAL INVESTIGATIONS OF DIFFERENT ORDERS OF RELATIVISTIC EFFECTS IN ATOMIC SHELLS

Different orders in alpha(2) of the hydrogenic energy levels are discu ssed. The spurious contribution of -0.2Z(5) alpha(3) of the first orde r Douglas-Kroll-Hess (DKH) Hamiltonian is cancelled at the second orde r DKH level, which recovers the energy up to the order of Z(6) alpha(4 ) at least to a large extent and includes also a significant part of t he higher order terms. Concerning the valence shell energies of many e lectron atoms, their behavior is more similar to the one of the hydrog en-like Is than of the respective nlj levels. The convergence of the a lpha(2) expansion becomes unsatisfactory for the very heavy elements.